On the geometry of aggregate snowflakes

TL;DR

This work addresses the mismatch between traditional, mean-geometry snowflake representations and the actual wide variability of aggregate snowflakes by developing a physics-based, stochastic parameterization of aggregate geometry. It generates millions of synthetic aggregates from a detailed 3D aggregation model and derives joint distributions for the key geometric descriptors ${D}_\text{norm}$, ${\phi}$, and $q$, which are then integrated into a Lagrangian particle framework as pseudo-prognostic variables. The approach demonstrates that a lognormal description of ${D}_\text{norm}$, together with habit-dependent parameterizations for ${D}_\text{max}$, ${\phi}$, and $q$, captures essential variability, modestly increases ensemble fall speeds, enhances aggregation, and broadens radar signatures in forward-model simulations. The results offer a path toward more realistic ice microphysics in weather and climate models and improved interpretation of multi-frequency radar observations, while highlighting the need for memory effects, habit-dependent sticking, and observational validation in future work.

Abstract

Snowflakes play a crucial role in weather and climate. A significant portion of precipitation that reaches the surface originates as ice, even when it ultimately falls as rain. Contrary to the popular image of symmetric, dendritic crystals, most large snowflakes are irregular aggregates formed through the collision of primary ice crystals, such as hexagonal plates, columns, and dendrites. These aggregates exhibit complex, fractal-like structures, particularly at large sizes. Despite this structural complexity, each aggregate snowflake is unique, with properties that vary significantly around the mean - variability that is typically neglected in weather and climate models. Using a physically based aggregation model, we generate millions of synthetic snowflakes to investigate their geometric properties. The resulting dataset reveals that, for a given monomer number (cluster size) and mass, the maximum dimension follows approximately a lognormal distribution. We present a parameterization of aggregate geometry that captures key statistical properties, including maximum dimension, aspect ratio, cross-sectional area, and their joint correlations. This formulation enables a stochastic representation of aggregate snowflakes in Lagrangian particle models. Incorporating this variability improves the realism of simulated fall velocities, enhances growth rates by aggregation, and broadens Doppler radar spectra in closer agreement with observations.

Figures (16)

• Figure 1: Scatter plots showing the mass-size relations for aggregates of needles, plates, and dendrites. Colors indicate monomer number $N$, and the regression line represents the power-law fit with fractal exponent $p$ for $N>5$.
• Figure 2: Histograms of the nondimensional maximum dimension $\hat{D}_\text{max}$ for aggregates of needles and aggregates of plates for different monomer numbers $N$. Solid lines represent lognormal distributions with the same mean and standard deviation as the data. The dendrite dataset looks similar and is not shown.
• Figure 3: Examples of aggregates of needles, aggregates of plates and aggregates of dendrites for monomer number $N=64$ and different ${D}_\text{norm}$. For each aggregate, the normalized diameter ${D}_\text{norm}$, the mass $m$ in kg, and the maximum dimension ${D}_\text{max}$ in m is given. The snowflakes with ${D}_\text{norm} < 1$ (left column) are much smaller in terms of maximum dimension ${D}_\text{max}$ than the elongated snowflakes with ${D}_\text{max} > 1$ (right column). The central column shows an example of the mean aggregates snowflake with ${D}_\text{norm}=1$ for the given $N$. The aggregate mass $m$ in each row is similar, but not identical.
• Figure 4: As Figure \ref{['fig:small-agg-examples']}, but for a monomer number of $N=1024$.
• Figure 5: Standard deviation of the normalized diameter ${D}_\text{norm}$ as a function of monomer number $N$ for aggregates of plates, aggregates of needles, and mixture aggregates of plates and needles (left), and aggregates of needles, aggregates of dendrites, and mixture aggregates of both (right). Aggregates of mixtures are shown for different monomer ratios $\mathit{MR}$. The solid lines are the parameterizations using Eqs. \ref{['eq:sigma0']}--\ref{['eq:sigma_mix2']}.